I have no idea how to figure this out... please help.
This question tests your knowledge of the distributive property of algebra.
Symbolically, the distributive property can be explained as follows:
x*(y + z) = (x*y) + (x*z) = xy + xz, or alternatively
x*(y - z) = (x*y) - (x*z)
...where x, y, and z are numbers (real, rational, etc.). In words, when you multiply a number by the sum or difference of a group of terms,
x * (y + z)
then you can convert this into the sum or difference of x "times" each of those individual terms. On the right hand side of the first equation,
x*y + x*z
You see how the "+" symbol stays in place, and both y and z are multiplied by x separately. Then you just have to add the two terms to get your answer! (Of course, you must first perform the multiplication of x*y and x*z to know what you are adding.)
So let's use the distributive property to solve your question, which I will restate:
4w - 9(6 - 5w) = 44
Ignoring the "4w" term for a moment, let's use the distributive property to expand the "9(6 - 5w)". Using what we learned above, you want to multiply 9 by 6, place your "-" sign after it, then multiply 9 by 5w. This will give us
9(6 - 5w) = (9*6) - (9 * 5w)
Note that the expression on the right side is now a difference of two terms, which after multiplication, can be simplified to
(9*6) - (9 * 5w) = (54) - (45w) = 54 - 45w
And w, as you may know, is a variable in this case...it should be treated like a regular number (so any operation can be performed on it, like multiplication), but you don't know it's value yet. Thus 9*5w is the same as 9*5*w, which is 45*w = 45w.
Anyway, after that expansion using the distributive property, you have
4w - (54 - 45w) = 44
Which is another way of writing
4w + (-1)*(54 - 45w) = 44
because when you subtract a number, it is the same process as adding that number "times" -1.
So we use the distributive property AGAIN to get
4w + (-1*54) - (-1*45w) = 4w + (-54) - (-45w) = 4w - 54 + 45w
Now I will state your initial question one final time, given that I found an easier way to express "4w - 9(6 - 5w)" :
4w - 54 + 45w = 44
At this point you combine "like terms", so on the left hand side of the equation you would add 4w and 45w to get 49w.
(4w + 45w) - 54 = 44 ---> 49w - 54 = 44
Next you add 54 to both sides of the equation
49w - 54 + 54 = 44 + 54
49w = 98
As a final step, you divide both sides by 49, to get w alone on one side (which gives you the value of w!)
49 * w / 49 = 98 / 49
(49 / 49) * w = (98 / 49)
1 * w = 2
w = 2
And there you have it... the solution to this problem is w = 2.
Hope this helps! And if anything in this explanation needs clarification, don't be afraid to ask!